{
  "abstract": "Based on a 1981 work by G. Talenti, which established a comparison principle for smooth solutions of the Monge-Ampère equation alongside related two-dimensional a priori estimates, this paper explores the connection to the Blaschke-Santaló inequality and its reverse form by K. Mahler (1939). More specifically, in this work, a quantitative version of one of Talenti's a priori estimates is proved. We exploit the interplay between Talenti's analytical framework and Mahler/Blaschke-Santaló inequalities via convex geometry, demonstrating how this link can be utilized to gain sharp insights into the Alexandrov-Bakelman-Pucci (ABP) maximum principle for elliptic PDEs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.24388",
  "author_total": 1,
  "authors": [
    {
      "name": "Antonio Porricelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjrams0jh8259.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.24388",
  "fulltext_url": null,
  "id": "fjrams0jh8259",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.24388",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.24388",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fjrams0jh8259.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2607.24388",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.24388"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Sharpness and Planar Stability of the Alexandrov-Bakelman-Pucci Estimate: a Convex Geometric Approach",
  "title_text": "Sharpness and Planar Stability of the Alexandrov-Bakelman-Pucci Estimate: a Convex Geometric Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/fjrams0jh8259",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s11587-026-01184-8",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}